Consider the following Linear Programming Problem

Question

Consider the following Linear Programming Problem: A school district is buying new buses to transport students in Winnipeg. There are two types of buses available: the Bronco buses and the Neon buses. Each Bronco bus costs 18,000 dollars has a capacity of 25 passengers, and will require 2 mechanical repairs per year. Each Neon bus costs 22,000 dollars has a capacity of 30 passengers, and will require 1 mechanical repair per year. The school district has a budget of $594,000, and can afford at most 40 mechanical repairs per year. Due to storage space, the school district cannot buy more than 32 buses. How many buses of each type should the school district buy in order to maximize the number of students that the buses can transport?

e) How many buses of each type should be bought in order to meet the requirements and conditions maximizing the number of passengers? What is the maximum number of passengers possible?

Answer 1

Hello, Jacob,

Let's set the number of Bronco buses to x and the number of neon buses to y. We can form the following equations based on the total budget, repairs/year, and storage limit:

Total Budget: 18000x + 22000y <= 594,000

Parking limit: x + y <= 32

Mech Repair/yr: 2x + 1y <=40

Graphing these three lines on DESMOS. I find an intersection at (11,18) where all conditions are met. I'm not certain how this information can be used to optimize for the number of students, however. 11 Bronco ands 18 Neon buses will accomodate 11*25 + 18*30 = 995 passengers.

Somehow, the equation 25x + 30y must be maximized to find the best combination of buses that meet the financial and parking requirements, and have the greatest passenger capacity. Sorry - I'm not sure how that can be done.

Bob